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Homework Help: AC Voltage

  1. Nov 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Given an AC Voltage that varies in time according to the equation:

    v(t) = 100 sin(250t)

    (i) What is the frequency of this waveform?

    (ii) Calculate the time for one complete cycle of the voltage?

    (iii) Calculate the instantaneous value of the voltage at time = 6ms.

    (iv) Calculate the Root-Mean Square (RMS) value of the AC voltage.

    (v) The first time after t=0ms that the instantaneous voltage is 50V.

    2. Relevant equations

    v(t) sin (250 x 6 x 10^-3)

    3. The attempt at a solution

    I'm trying to, obviously, get the third part of this. What I have so far is:
    100sin (250pi x 6 x 10^-3)
    =100sin (4.71)
    In an example in my book it then goes on to multiply 100 x .951... where does the .951 come from and is this what I use for this equation or should I use a different number?
    The equation in the book I have is (still 6ms):
    v(t) = 100sin (100pi t) V
    Their solution is:
    100 sin (100pi x 6 x 10^-3)
    =100sin (1.88)
    =100 x .951
    Not sure what I'm missing?
  2. jcsd
  3. Nov 3, 2012 #2


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    It looks like they are using ##100\pi## instead of the ##250\pi##. Probably a typo somewhere.
  4. Nov 4, 2012 #3


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    sin(1.8849) = 0.951 if using radians.

    In your problem (which is different to the one in the book) you use a different number eg..

    = 100sin(4.71)
  5. Nov 4, 2012 #4
    OH I see, just got confused. Thank you!!
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